Severe gale-force winds were battering large parts of New Zealand's South Island on Tuesday, bringing down trees, tearing roofs from buildings, and cutting power to thousands of homes and businesses.

Dunedin Airport is closed and flood warnings have been issued for Southland and Canterbury.

One of the worst-affected areas for power is the Selwyn District west of Christchurch, where lines company Orion said about 5,000 homes are without electricity, Radio New Zealand reported on Tuesday.

Alpine Energy said about 1,200 homes in South Canterbury still don't have electricity, and it expects 500 will spend the night without power.

Aurora Energy said electricity supply was briefly cut to almost 1,700 properties in Arrowtown, Dalefield and Coronet Peak after a lightning strike.

It said a small number of homes are still without power in Mosgiel south of Dunedin.

Network Waitaki said about 100 customers, including in Oamaru, remain without power. It said strong wind has brought down trees and on to power lines.

The company said the strong winds are preventing some lines from being restored and some people could be without power for the night.

Flights were cancelled or diverted at Dunedin Airport on Tuesday afternoon, with chief executive John McCall saying winds across the runways were too strong. He says it is up to airlines to decide when to resume flights.

MetService said the strongest winds will be felt in inland parts of Canterbury, with gusts of up to 140 kilometres per hour and heavy rain expected on the West Coast.

Police said two trucks were blown over by high winds on State Highway 1, north of Dunedin.

They said one driver was treated for minor injuries by ambulance at that scene, about 20 km north of Dunedin. The other truck blew over south of Oamaru.

Severe weather warnings are in place for all of New Zealand south of Taranaki and Gisborne.

Canterbury Regional Council has issued flood warnings for the Rakaia, Waimakariri, Hurunui and Waiau rivers.